A model describing the role of transversal and longitudinal diffusion of cGMP and Ca2+ in signaling in the rod outer segment of vertebrates is developed. Utilizing a novel notion of surface-volume reaction and the mathematical theories of homogenization and concentrated capacity, the diffusion of cGMP CGMP and Ca2+ in the interdiscal spaces is shown to be reducible to a one-parameter family of diffusion processes taking place on a single rod cross section; whereas the diffusion in the outer shell is shown to be reducible to a diffusion on a cylindrical surface. Moreover, the exterior flux of the former serves as a source term for the latter, alleviating the assumption of a well-stirred cytosol. A previous model of visual transduction that assumes a well-stirred rod outer segment cytosol (and thus contains no spatial information) can be recovered from this model by imposing a "bulk" assumption. The model shows that upon activation of a single rhodopsin, cGMP changes are local, and exhibit both a longitudinal and a transversal component. Consequently, membrane current is also highly localized. The spatial spread of the single photon response along the longitudinal axis of the outer segment is predicted to be 3-5 μm, consistent with experimental data. This approach represents a tool to analyze pointwise signaling dynamics without requiring averaging over the entire cell by global Michaelis-Menten kinetics.
Andreucci, D., Bisegna, P., Caruso, G., Hamm, H.e., Dibenedetto, E. (2003). Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction. BIOPHYSICAL JOURNAL, 85(3), 1358-1376 [10.1016/S0006-3495(03)74570-6].
Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction
BISEGNA, PAOLO;
2003-01-01
Abstract
A model describing the role of transversal and longitudinal diffusion of cGMP and Ca2+ in signaling in the rod outer segment of vertebrates is developed. Utilizing a novel notion of surface-volume reaction and the mathematical theories of homogenization and concentrated capacity, the diffusion of cGMP CGMP and Ca2+ in the interdiscal spaces is shown to be reducible to a one-parameter family of diffusion processes taking place on a single rod cross section; whereas the diffusion in the outer shell is shown to be reducible to a diffusion on a cylindrical surface. Moreover, the exterior flux of the former serves as a source term for the latter, alleviating the assumption of a well-stirred cytosol. A previous model of visual transduction that assumes a well-stirred rod outer segment cytosol (and thus contains no spatial information) can be recovered from this model by imposing a "bulk" assumption. The model shows that upon activation of a single rhodopsin, cGMP changes are local, and exhibit both a longitudinal and a transversal component. Consequently, membrane current is also highly localized. The spatial spread of the single photon response along the longitudinal axis of the outer segment is predicted to be 3-5 μm, consistent with experimental data. This approach represents a tool to analyze pointwise signaling dynamics without requiring averaging over the entire cell by global Michaelis-Menten kinetics.File | Dimensione | Formato | |
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